The reason you can't find the order number in Blesta's search is due to it being related to the Order plugin. The Order plugin doesn't provide search functionality (maybe it should), so you couldn't find it from there.
However, you can find it in the order widget. Under [billing] -> [Overview], an Orders widget is available. If you don't already have that enabled, you should click to "Manage Widgets" and add it to your billing overview dashboard. It will list orders that are pending, accepted, etc., and will show the order number you're looking for, which is what the client sees on the confirmation page.